Abstract

The chirp of single-cycle microwave fields after interaction with pairs of parallel diffraction gratings is measured in a phase-sensitive terahertz spectrometer. Novel transmission grating pairs recently proposed by Tournois, which combine diffraction and refraction effects, yield an almost linear group delay over a bandwidth that exceeds that of conventional reflection gratings by a factor of ~3.5. The experimentally measured group delay shows good agreement with theoretical predictions for both types of grating. The applicability of the novel transmission gratings for stretching and compression of 1–2-fs pulses in the optical regime and the limitations set by material dispersion are discussed.

© 1995 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |

  1. P. Maine, D. Strickland, P. Bado, M. Pessot, and G. Mourou, IEEE J. Quantum Electron. 24, 398 (1988).
    [CrossRef]
  2. B. Broers, H. B. van Linden van den Heuvell, and L. D. Noordam, Phys. Rev. Lett. 69, 2062 (1992).
    [CrossRef] [PubMed]
  3. J. A. Valdmanis, "Real time picosecond optical oscilloscope," in Ultrafast Phenomena V, G. R. Fleming and A. E. Siegman, eds. (Springer-Verlag, Berlin, 1986), p. 82.
    [CrossRef]
  4. A. M. Weiner, D. E. Leaird, D. H. Reitze, and E. G. Paek, Opt. Lett. 17, 224 (1992).
    [CrossRef] [PubMed]
  5. M. C. Tatham, G. Sherlock, and L. D. Westbrook, Electron. Lett. 29, 1851 (1993).
    [CrossRef]
  6. R. R. Jones, D. You, and P. H. Bucksbaum, Phys. Rev. Lett. 70, 1236 (1993).
    [CrossRef] [PubMed]
  7. J. X. Tull, C. W. Hillegas, D. Goswami, and W. S. Warren, "Molecular pulse shaping," in Ultrafast Phenomena IX (Springer-Verlag, Berlin, 1994), p. 553.
  8. E. B. Treacy, IEEE J. Quantum Electron. 5, 454 (1969). The group delay that we use differs slightly from the formula in the cited paper, to conform to the notation and the convention for defining τ used by Tournois. The difference is only a constant.
    [CrossRef]
  9. R. L. Fork, C. H. Brito Cruz, P. C. Becker, and C. V. Shank, Opt. Lett. 12, 483 (1987).
    [CrossRef] [PubMed]
  10. J. M. Simon, S. A. Ledesma, C. C. Iemmi, and O. E. Martinez, Opt. Lett. 16, 1704 (1994).
    [CrossRef]
  11. P. Tournois, Electron. Lett. 29, 1414 (1993).
    [CrossRef]
  12. A. Stingl, Ch. Spielmann, F. Krausz, and R. Szipöcs, Opt. Lett. 19, 204 (1994).
    [CrossRef] [PubMed]
  13. J. Zhou, G. Taft, C.-P. Huang, M. M. Murnane, H. C. Kapteyn, and I. P. Christov, Opt. Lett. 15, 1149 (1994).
    [CrossRef]
  14. D. Grischkowsky, S. Keiding, M. van Exter, and C. Fattinger, J. Opt. Soc. Am. 7, 2006 (1990).
    [CrossRef]
  15. J. Paye, IEEE J. Quantum Electron. 28, 2262 (1992).
    [CrossRef]
  16. This interpretation is complicated somewhat by the fact that W can take negative values.
  17. J. Paye, M. Ramaswamy, J. G. Fugimoto, and E. P. Ippen, Opt. Lett. 18, 1946 (1993).
    [CrossRef] [PubMed]
  18. E. Özbay, E. Michel, G. Tuttle, R. Biswas, K. M. Ho, J. Bostak, and D. M. Bloom, Opt. Lett. 19, 1155 (1994).
    [CrossRef] [PubMed]

Bado, P.

P. Maine, D. Strickland, P. Bado, M. Pessot, and G. Mourou, IEEE J. Quantum Electron. 24, 398 (1988).
[CrossRef]

Becker, P. C.

R. L. Fork, C. H. Brito Cruz, P. C. Becker, and C. V. Shank, Opt. Lett. 12, 483 (1987).
[CrossRef] [PubMed]

Biswas, R.

E. Özbay, E. Michel, G. Tuttle, R. Biswas, K. M. Ho, J. Bostak, and D. M. Bloom, Opt. Lett. 19, 1155 (1994).
[CrossRef] [PubMed]

Bloom, D. M.

E. Özbay, E. Michel, G. Tuttle, R. Biswas, K. M. Ho, J. Bostak, and D. M. Bloom, Opt. Lett. 19, 1155 (1994).
[CrossRef] [PubMed]

Bostak, J.

E. Özbay, E. Michel, G. Tuttle, R. Biswas, K. M. Ho, J. Bostak, and D. M. Bloom, Opt. Lett. 19, 1155 (1994).
[CrossRef] [PubMed]

Broers, B.

B. Broers, H. B. van Linden van den Heuvell, and L. D. Noordam, Phys. Rev. Lett. 69, 2062 (1992).
[CrossRef] [PubMed]

Bucksbaum, P. H.

R. R. Jones, D. You, and P. H. Bucksbaum, Phys. Rev. Lett. 70, 1236 (1993).
[CrossRef] [PubMed]

Christov, I. P.

J. Zhou, G. Taft, C.-P. Huang, M. M. Murnane, H. C. Kapteyn, and I. P. Christov, Opt. Lett. 15, 1149 (1994).
[CrossRef]

Cruz, C. H. Brito

R. L. Fork, C. H. Brito Cruz, P. C. Becker, and C. V. Shank, Opt. Lett. 12, 483 (1987).
[CrossRef] [PubMed]

Exter, M. van

D. Grischkowsky, S. Keiding, M. van Exter, and C. Fattinger, J. Opt. Soc. Am. 7, 2006 (1990).
[CrossRef]

Fattinger, C.

D. Grischkowsky, S. Keiding, M. van Exter, and C. Fattinger, J. Opt. Soc. Am. 7, 2006 (1990).
[CrossRef]

Fork, R. L.

R. L. Fork, C. H. Brito Cruz, P. C. Becker, and C. V. Shank, Opt. Lett. 12, 483 (1987).
[CrossRef] [PubMed]

Fugimoto, J. G.

J. Paye, M. Ramaswamy, J. G. Fugimoto, and E. P. Ippen, Opt. Lett. 18, 1946 (1993).
[CrossRef] [PubMed]

Goswami, D.

J. X. Tull, C. W. Hillegas, D. Goswami, and W. S. Warren, "Molecular pulse shaping," in Ultrafast Phenomena IX (Springer-Verlag, Berlin, 1994), p. 553.

Grischkowsky, D.

D. Grischkowsky, S. Keiding, M. van Exter, and C. Fattinger, J. Opt. Soc. Am. 7, 2006 (1990).
[CrossRef]

Heuvell, H. B. van Linden van den

B. Broers, H. B. van Linden van den Heuvell, and L. D. Noordam, Phys. Rev. Lett. 69, 2062 (1992).
[CrossRef] [PubMed]

Hillegas, C. W.

J. X. Tull, C. W. Hillegas, D. Goswami, and W. S. Warren, "Molecular pulse shaping," in Ultrafast Phenomena IX (Springer-Verlag, Berlin, 1994), p. 553.

Ho, K. M.

E. Özbay, E. Michel, G. Tuttle, R. Biswas, K. M. Ho, J. Bostak, and D. M. Bloom, Opt. Lett. 19, 1155 (1994).
[CrossRef] [PubMed]

Huang, C.-P.

J. Zhou, G. Taft, C.-P. Huang, M. M. Murnane, H. C. Kapteyn, and I. P. Christov, Opt. Lett. 15, 1149 (1994).
[CrossRef]

Iemmi, C. C.

J. M. Simon, S. A. Ledesma, C. C. Iemmi, and O. E. Martinez, Opt. Lett. 16, 1704 (1994).
[CrossRef]

Ippen, E. P.

J. Paye, M. Ramaswamy, J. G. Fugimoto, and E. P. Ippen, Opt. Lett. 18, 1946 (1993).
[CrossRef] [PubMed]

Jones, R. R.

R. R. Jones, D. You, and P. H. Bucksbaum, Phys. Rev. Lett. 70, 1236 (1993).
[CrossRef] [PubMed]

Kapteyn, H. C.

J. Zhou, G. Taft, C.-P. Huang, M. M. Murnane, H. C. Kapteyn, and I. P. Christov, Opt. Lett. 15, 1149 (1994).
[CrossRef]

Keiding, S.

D. Grischkowsky, S. Keiding, M. van Exter, and C. Fattinger, J. Opt. Soc. Am. 7, 2006 (1990).
[CrossRef]

Krausz, F.

A. Stingl, Ch. Spielmann, F. Krausz, and R. Szipöcs, Opt. Lett. 19, 204 (1994).
[CrossRef] [PubMed]

Leaird, D. E.

A. M. Weiner, D. E. Leaird, D. H. Reitze, and E. G. Paek, Opt. Lett. 17, 224 (1992).
[CrossRef] [PubMed]

Ledesma, S. A.

J. M. Simon, S. A. Ledesma, C. C. Iemmi, and O. E. Martinez, Opt. Lett. 16, 1704 (1994).
[CrossRef]

Maine, P.

P. Maine, D. Strickland, P. Bado, M. Pessot, and G. Mourou, IEEE J. Quantum Electron. 24, 398 (1988).
[CrossRef]

Martinez, O. E.

J. M. Simon, S. A. Ledesma, C. C. Iemmi, and O. E. Martinez, Opt. Lett. 16, 1704 (1994).
[CrossRef]

Michel, E.

E. Özbay, E. Michel, G. Tuttle, R. Biswas, K. M. Ho, J. Bostak, and D. M. Bloom, Opt. Lett. 19, 1155 (1994).
[CrossRef] [PubMed]

Mourou, G.

P. Maine, D. Strickland, P. Bado, M. Pessot, and G. Mourou, IEEE J. Quantum Electron. 24, 398 (1988).
[CrossRef]

Murnane, M. M.

J. Zhou, G. Taft, C.-P. Huang, M. M. Murnane, H. C. Kapteyn, and I. P. Christov, Opt. Lett. 15, 1149 (1994).
[CrossRef]

Noordam, L. D.

B. Broers, H. B. van Linden van den Heuvell, and L. D. Noordam, Phys. Rev. Lett. 69, 2062 (1992).
[CrossRef] [PubMed]

Özbay, E.

E. Özbay, E. Michel, G. Tuttle, R. Biswas, K. M. Ho, J. Bostak, and D. M. Bloom, Opt. Lett. 19, 1155 (1994).
[CrossRef] [PubMed]

Paek, E. G.

A. M. Weiner, D. E. Leaird, D. H. Reitze, and E. G. Paek, Opt. Lett. 17, 224 (1992).
[CrossRef] [PubMed]

Paye, J.

J. Paye, IEEE J. Quantum Electron. 28, 2262 (1992).
[CrossRef]

J. Paye, M. Ramaswamy, J. G. Fugimoto, and E. P. Ippen, Opt. Lett. 18, 1946 (1993).
[CrossRef] [PubMed]

Pessot, M.

P. Maine, D. Strickland, P. Bado, M. Pessot, and G. Mourou, IEEE J. Quantum Electron. 24, 398 (1988).
[CrossRef]

Ramaswamy, M.

J. Paye, M. Ramaswamy, J. G. Fugimoto, and E. P. Ippen, Opt. Lett. 18, 1946 (1993).
[CrossRef] [PubMed]

Reitze, D. H.

A. M. Weiner, D. E. Leaird, D. H. Reitze, and E. G. Paek, Opt. Lett. 17, 224 (1992).
[CrossRef] [PubMed]

Shank, C. V.

R. L. Fork, C. H. Brito Cruz, P. C. Becker, and C. V. Shank, Opt. Lett. 12, 483 (1987).
[CrossRef] [PubMed]

Sherlock, G.

M. C. Tatham, G. Sherlock, and L. D. Westbrook, Electron. Lett. 29, 1851 (1993).
[CrossRef]

Simon, J. M.

J. M. Simon, S. A. Ledesma, C. C. Iemmi, and O. E. Martinez, Opt. Lett. 16, 1704 (1994).
[CrossRef]

Spielmann, Ch.

A. Stingl, Ch. Spielmann, F. Krausz, and R. Szipöcs, Opt. Lett. 19, 204 (1994).
[CrossRef] [PubMed]

Stingl, A.

A. Stingl, Ch. Spielmann, F. Krausz, and R. Szipöcs, Opt. Lett. 19, 204 (1994).
[CrossRef] [PubMed]

Strickland, D.

P. Maine, D. Strickland, P. Bado, M. Pessot, and G. Mourou, IEEE J. Quantum Electron. 24, 398 (1988).
[CrossRef]

Szipöcs, R.

A. Stingl, Ch. Spielmann, F. Krausz, and R. Szipöcs, Opt. Lett. 19, 204 (1994).
[CrossRef] [PubMed]

Taft, G.

J. Zhou, G. Taft, C.-P. Huang, M. M. Murnane, H. C. Kapteyn, and I. P. Christov, Opt. Lett. 15, 1149 (1994).
[CrossRef]

Tatham, M. C.

M. C. Tatham, G. Sherlock, and L. D. Westbrook, Electron. Lett. 29, 1851 (1993).
[CrossRef]

Tournois, P.

P. Tournois, Electron. Lett. 29, 1414 (1993).
[CrossRef]

Treacy, E. B.

E. B. Treacy, IEEE J. Quantum Electron. 5, 454 (1969). The group delay that we use differs slightly from the formula in the cited paper, to conform to the notation and the convention for defining τ used by Tournois. The difference is only a constant.
[CrossRef]

Tull, J. X.

J. X. Tull, C. W. Hillegas, D. Goswami, and W. S. Warren, "Molecular pulse shaping," in Ultrafast Phenomena IX (Springer-Verlag, Berlin, 1994), p. 553.

Tuttle, G.

E. Özbay, E. Michel, G. Tuttle, R. Biswas, K. M. Ho, J. Bostak, and D. M. Bloom, Opt. Lett. 19, 1155 (1994).
[CrossRef] [PubMed]

Valdmanis, J. A.

J. A. Valdmanis, "Real time picosecond optical oscilloscope," in Ultrafast Phenomena V, G. R. Fleming and A. E. Siegman, eds. (Springer-Verlag, Berlin, 1986), p. 82.
[CrossRef]

Warren, W. S.

J. X. Tull, C. W. Hillegas, D. Goswami, and W. S. Warren, "Molecular pulse shaping," in Ultrafast Phenomena IX (Springer-Verlag, Berlin, 1994), p. 553.

Weiner, A. M.

A. M. Weiner, D. E. Leaird, D. H. Reitze, and E. G. Paek, Opt. Lett. 17, 224 (1992).
[CrossRef] [PubMed]

Westbrook, L. D.

M. C. Tatham, G. Sherlock, and L. D. Westbrook, Electron. Lett. 29, 1851 (1993).
[CrossRef]

You, D.

R. R. Jones, D. You, and P. H. Bucksbaum, Phys. Rev. Lett. 70, 1236 (1993).
[CrossRef] [PubMed]

Zhou, J.

J. Zhou, G. Taft, C.-P. Huang, M. M. Murnane, H. C. Kapteyn, and I. P. Christov, Opt. Lett. 15, 1149 (1994).
[CrossRef]

Other

P. Maine, D. Strickland, P. Bado, M. Pessot, and G. Mourou, IEEE J. Quantum Electron. 24, 398 (1988).
[CrossRef]

B. Broers, H. B. van Linden van den Heuvell, and L. D. Noordam, Phys. Rev. Lett. 69, 2062 (1992).
[CrossRef] [PubMed]

J. A. Valdmanis, "Real time picosecond optical oscilloscope," in Ultrafast Phenomena V, G. R. Fleming and A. E. Siegman, eds. (Springer-Verlag, Berlin, 1986), p. 82.
[CrossRef]

A. M. Weiner, D. E. Leaird, D. H. Reitze, and E. G. Paek, Opt. Lett. 17, 224 (1992).
[CrossRef] [PubMed]

M. C. Tatham, G. Sherlock, and L. D. Westbrook, Electron. Lett. 29, 1851 (1993).
[CrossRef]

R. R. Jones, D. You, and P. H. Bucksbaum, Phys. Rev. Lett. 70, 1236 (1993).
[CrossRef] [PubMed]

J. X. Tull, C. W. Hillegas, D. Goswami, and W. S. Warren, "Molecular pulse shaping," in Ultrafast Phenomena IX (Springer-Verlag, Berlin, 1994), p. 553.

E. B. Treacy, IEEE J. Quantum Electron. 5, 454 (1969). The group delay that we use differs slightly from the formula in the cited paper, to conform to the notation and the convention for defining τ used by Tournois. The difference is only a constant.
[CrossRef]

R. L. Fork, C. H. Brito Cruz, P. C. Becker, and C. V. Shank, Opt. Lett. 12, 483 (1987).
[CrossRef] [PubMed]

J. M. Simon, S. A. Ledesma, C. C. Iemmi, and O. E. Martinez, Opt. Lett. 16, 1704 (1994).
[CrossRef]

P. Tournois, Electron. Lett. 29, 1414 (1993).
[CrossRef]

A. Stingl, Ch. Spielmann, F. Krausz, and R. Szipöcs, Opt. Lett. 19, 204 (1994).
[CrossRef] [PubMed]

J. Zhou, G. Taft, C.-P. Huang, M. M. Murnane, H. C. Kapteyn, and I. P. Christov, Opt. Lett. 15, 1149 (1994).
[CrossRef]

D. Grischkowsky, S. Keiding, M. van Exter, and C. Fattinger, J. Opt. Soc. Am. 7, 2006 (1990).
[CrossRef]

J. Paye, IEEE J. Quantum Electron. 28, 2262 (1992).
[CrossRef]

This interpretation is complicated somewhat by the fact that W can take negative values.

J. Paye, M. Ramaswamy, J. G. Fugimoto, and E. P. Ippen, Opt. Lett. 18, 1946 (1993).
[CrossRef] [PubMed]

E. Özbay, E. Michel, G. Tuttle, R. Biswas, K. M. Ho, J. Bostak, and D. M. Bloom, Opt. Lett. 19, 1155 (1994).
[CrossRef] [PubMed]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (13)

Fig. 1
Fig. 1

(a) Treacy reflection grating pair. (b) Tournois transmission grating pair.

Fig. 2
Fig. 2

Electric field of microwave pulse (a) incident upon and (b) transmitted through the Treacy grating.

Fig. 3
Fig. 3

Wigner function of microwave pulse (a) incident upon and (b) transmitted through the Treacy grating.

Fig. 4
Fig. 4

Phase (a) and group-delay (b) spectra for the Treacy grating.

Fig. 5
Fig. 5

Electric field (a) incident upon and (b)–(d) transmitted through the Tournois prism for different spacings.

Fig. 6
Fig. 6

Phase spectra for the Tournois grating at various angles of incidence.

Fig. 7
Fig. 7

Group-delay spectra for the Tournois grating for the same angles of incidence as in Fig. 6.

Fig. 8
Fig. 8

Wigner function of a microwave pulse stretched by the Tournois grating.

Fig. 9
Fig. 9

Operation of the Tournois grating for angles of incidence (a) less than, (b) equal to, and (c) greater than the critical angle.

Fig. 10
Fig. 10

Normalized group-delay spectra for the Tournois grating with various amounts of (a) linear and (b) quadratic dispersion.

Fig. 11
Fig. 11

Inflection frequency (infl. freq.) and high and low frequencies marking the extent of the linear region for the Tournois grating with various amounts of (a) linear and (b) quadratic dispersion.

Fig. 12
Fig. 12

Slope at the inflection point, multiplied by c/d, for the Tournois grating with various amounts of linear (solid curve) and quadratic (dashed curve) dispersion.

Fig. 13
Fig. 13

Amplitude spectra for a microwave pulse incident upon (dotted) and transmitted through (dashed) the Tournois grating.

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

W ( ω , t ) = E ( t + t / 2 ) E * ( t - t / 2 ) exp ( i ω t ) d t ,
k ( ω ) sin θ ( ω ) = k ( ω ) sin θ - 2 π p / a ,
ϕ ( ω ) = ω τ ( ω ) + ( 2 π d / a ) tan θ ( ω ) .
τ ( ω ) = [ d / c cos θ ( ω ) ] { 1 - cos [ θ - θ ( ω ) ] } .
k ( ω ) sin θ ( ω ) = k ( ω ) N sin θ - 2 π p / a .
τ R ( ω ) = [ d / c cos θ ( ω ) ] { 1 - N cos [ θ - θ ( ω ) ] } .
N = N 0 [ 1 + α ( ν - ν 0 ) + β ( ν - ν 0 ) 2 ] .
τ D = d c cos θ ( ω ) + N g ( ω ) d c { cos [ θ - θ ( ω hi ) ] cos θ ( ω hi ) - cos [ θ - θ ( ω ) ] cos θ ( ω ) }
= d c cos θ + N g d sin θ c ( tan θ hi - tan θ ) ,
δ = [ τ D ( ω ) - τ L ( ω ) ] / [ τ L ( ω ) - τ D ( ω 0 ) ] .

Metrics